scholarly journals On the affinely connected space admitting a group of affine motions

1950 ◽  
Vol 26 (4) ◽  
pp. 107-110 ◽  
Author(s):  
Yosio Mutō
Keyword(s):  
Connected Space ◽  
Affinely Connected Space

scholarly journals Recurrence Decompositions in Finsler Space

2020 ◽  
Vol 1 (1) ◽  
pp. 77-86
Author(s):  
Adel M. A. Al-Qashbari
Keyword(s):  
Differential Geometry ◽  
Covariant Derivative ◽  
Finsler Space ◽  
Applied Mathematics ◽  
Torsion Tensor ◽  
Finsler Geometry ◽  
Second Order ◽  
Connected Space ◽  
Projective Curvature Tensor ◽  
Affinely Connected Space

Finsler geometry is a kind of differential geometry originated by P. Finsler. Indeed, Finsler geometry has several uses in a wide variety and it is playing an important role in differential geometry and applied mathematics of problems in physics relative, manual footprint. It is usually considered as a generalization of Riemannian geometry. In the present paper, we introduced some types of generalized $W^{h}$ -birecurrent Finsler space, generalized $W^{h}$ -birecurrent affinely connected space and we defined a Finsler space $F_{n}$ for Weyl's projective curvature tensor $W_{jkh}^{i}$ satisfies the generalized-birecurrence condition with respect to Cartan's connection parameters $\Gamma ^{\ast i}_{kh}$, such that given by the condition (\ref{2.1}), where $\left\vert m\right. \left\vert n\right. $ is\ h-covariant derivative of second order (Cartan's second kind covariant differential operator) with respect to $x^{m}$ \ and $x^{n}$ ,\ successively, $\lambda _{mn}$ and $\mu _{mn~}$ are\ non-null covariant vectors field and such space is called as a generalized $W^{h}$ -birecurrent\ space and denoted briefly by $GW^{h}$ - $BRF_{n}$ . We have obtained some theorems of generalized $W^{h}$ -birecurrent affinely connected space for the h-covariant derivative of the second order for Wely's projective torsion tensor $~W_{kh}^{i}$ , Wely's projective deviation tensor $~W_{h}^{i}$ in our space. We have obtained the necessary and sufficient condition forsome tensors in our space.

scholarly journals On two linear vector spaces associated with a vector in an Ln

1940 ◽  
Vol 6 (3) ◽  
pp. 172-175
Author(s):  
Yung-Chow Wong
Keyword(s):  
Vector Field ◽  
Vector Spaces ◽  
Connected Space ◽  
Covariant Differentiation ◽  
Linear Vector ◽  
The Matrix ◽  
Image Position ◽  
Affinely Connected Space

Let υλ be a vector (i.e. a vector field) in an affinely connected space Ln, ∇k the symbol of covariant differentiation, and r the rank of the matrix ‖∇k υλ‖ then there exist two sets of n − r independent vectors and which satisfy respectively the equations

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